Construction of highly non-linear cubic homogeneous Boolean functions on GF2n+l (2)

Authors

Jing Wu, University of WollongongFollow
Tianbing Xia, University of WollongongFollow
Jennifer Seberry, University of WollongongFollow

RIS ID

9399

Publication Details

This article was originally published as Construction of highly non-linear cubic homogeneous Boolean functions on GF2n+l (2), in Arabnia, HR, Mun, Y and Aissi, S (eds), Proceedings of the 2003 International Conference on Security and management (SAM'03), Las Vegas, 23-26 June 2003, 241-247.

Abstract

The work studies highly nonlinear Boolean functions in GF2n+1(2), i.e. for the dimensions where bent functions do not exist. We prove that for every n > 2 there exist homogeneous Boolean functions on GF(2)2n+1 with non-linearity greater than or equal to 22n — 2n and without linear structures.